$g(x)=3-x^2$ $h(x)=4-3x$ Write $(g\circ h)(x)$ as an expression in terms of $x$. $(g\circ h)(x)=$
First, let's write $(g\circ h)(x)$ as $g(h(x))$. Next, we write $h(x)$ as the input to function $g$. $g({h(x)})=3-({h(x)})^2$ Since $h(x)=4-3x$, this becomes: $\begin{aligned} g({h(x)})&=3-({4-3x})^2\\ \\ &=3-(16-24x+9x^2)\\ \\ &=3-16+24x-9x^2\\ \\ &=-9x^2+24x-13\\ \end{aligned}$ Note: We simplified the result to obtain a nicer expression, but this is not necessary. The answer: $(g\circ h)(x)=-9x^2+24x-13$